I wouldn’t say so, no - and I’m someone who’s not at all keen on most very popular names.
I do know a few young Phoebes, but where I am it’s much less overused than the ubiquitous Ava/Ada/Eva/Edie/Evie/Ivy/Isla, or Lily/Lila/Lyra/Layla/Luna type names. It’s also not especially similar to any other currently popular names, so unlike those mentioned you won’t get sucked into any particular ‘sound trend’.
Lovely meaning too - I say go for it. 🙂